... As well, the space being, an thermodynamically open system, if the heating elements should be spread about, the diffusion of their heat into the environment beyond the space is, effectively, assisted. Were one to move them closer together, they would, at certain proximities, cease to function.
Yes this is very true. This brings me to my next point. Using electricity for space heating by its very nature only makes sense if the heat is needed for a
decentralized application. The heat at the power station is in many cases just waste heat. It is here where space heating creates a further advantage for POW that was not taken into account even by Satoshi Nakamoto in
https://bitcoin.org/bitcoin.pdf or by Adam Back in
http://www.hashcash.org/papers/hashcash.pdf. The assumption that is made in these papers is that the marginal cost of POW is the same for the honest nodes as for an attacker (dishonest node). Space heating skews this further in favour of the honest nodes because the value of the heat is so much higher for the decentralized (honest nodes) than for the centralized (dishonest node). In short the honest nodes may end up having a negative marginal POW cost while a dishonest attacking node still has a positive marginal POW cost.
Making POW "useful" only makes sense only if the "useful" application
requires decentralization in order to have value. .
However, the economic merits of your proposition do not extend to those that do not
have regular access to a Bitcoin ASIC.